This is the 222nd most frequent Estonian word.
mu
"Mu" in Estonian means "my" or "mine."
Here 'mu' is used as a possessive determiner to indicate that the noun (nimi, 'name') belongs to the speaker.
Mu nimi on Anna.
My name is Anna.
In this context, 'mu' is showing possession of the noun (vanaema, 'grandmother'), also belonging to the speaker.
Mu vanaema küpsetas koogi.
My grandmother baked a cake.
Similarly, 'mu' indicates possession of the noun (lemmik raamat, 'favorite book'), showing it as related to the speaker.